In a modest flat in Visoko, near Sarajevo in Bosnia-Herzegovina, 12-year-old Adnan Nevic is playing with a globe. "America, Australia, Asia," he says, pointing out the places he would like to visit on the slightly deflated blow-up toy.

His favourite subject at school is geography and he wants to be a pilot when he grows up, the better to fulfil his dreams of global travel.

That Adnan has such an international outlook is hardly surprising: at only two days old, he was held aloft in a Sarajevo hospital by the then United Nations secretary general, Kofi Annan, to be snapped by the world's news photographers.

The UN calculates that the world will have its seventh billion person on 31 October; the global population will hit nine billion by 2050; and, according to a UN report due on Wednesday, by the end of the century there could be 16 billion people on the planet, although most experts consider this an unlikely scenario, at the very top end of the range of expectations.

Adnan was born in 1999, chosen ostensibly at random but really as a symbol of hope after a bloody decade in the former Yugoslavia, which was also the birthplace of the five billionth baby, born in Zagreb in 1987.

The four billionth person was born in 1974, and the three billionth in 1960, according to the UN.

Before that, the world took much longer to add so many people: there were two billion people in 1927, and it took the whole of human history until 1804 to reach the point at which a whole billion people inhabited the planet at the same time.

Adnan, as well as being a 12-year-old boy with aspirations to travel the globe, is an emblem of the rapidly growing world population that until recently has shown few signs of abating.

Rising birth rates in many countries, particularly in the developing world, have combined with longer life expectancy and successes in reducing infant mortality to produce a total population that few used to predict was even possible.

Adnan lives in a modest flat in the historic city. The cars parked outside are mid-range models not more than a few years old, the blocks are well-kept and the surroundings are pleasant though not affluent. Outside the block there is a solitary piece of graffiti, in blue spraypaint. It reads "Adnan". He is a local celebrity.

Most of the 78 million children born this year – and of the two to three billion expected in the next 40 years – will not be so lucky. The vast majority will be born into appalling privation, in slums in developing countries.

Is the world failing these children?

Last year, although enough food was produced to satisfy the world's needs, at least one billion people went hungry, according to UN estimates.

The same number lacked access to clean water and more than 2.6 billion people still have no adequate sanitation. Most of the world's population now live in towns and cities, not the countryside, for the first time in history. But the urban centres that people are joining are the world's burgeoning megacities, in each of which tens of millions of people live in penury without electricity, water, toilets or enough to eat.

Child seven billion will be born into a different world to that which Adnan entered – one threatened by terrorism, economic crisis, climate change and new wars unthought of in 1999. But the problems that the exploding population will unleash may, according to some commentators, make today's crises seem mild.

Kofi Annan holds newborn Adnan Nevic. Photograph: Reuters

"Of all the interconnected problems we face, perhaps the most serious is the proliferation of our own species," says Sir Crispin Tickell, a former British ambassador to the UN, now an environmental guru. "We are like a species out of control."

As population rises, this argument runs, consumption will increase and place an impossible strain on natural resources, from water supplies and agricultural land to fish in the ocean, as well as giving rise to runaway climate change as we burn ever more fossil fuels.

One example of the kind of problem the planet will face has been this year's devastating famine in the Horn of Africa. Drought was the primary cause, but it has been exacerbated by pressure on the land; the population of the region has doubled since the early 1970s.

Mary Robinson, the former Irish president, told a recent meeting of the Aspen Institute: "Somalia shows the extent to which failure to learn from the famine in 1992, and our failure to prioritise the health of women and children, has become a global problem, one none of us can ignore."

This view is derided in some quarters, especially the US right, as "neo-Malthusian" – a pessimistic assumption of limit to the world's bounty that has always been proved wrong in the past. Productivity – squeezing more food from less land, more energy from fewer resources – has kept pace with or exceeded population growth in the past, so why not in the future?

Although fertility rates have declined slightly from their 1960s peak, there is now a demographic "bulge", a boom in the number of young people, that will ensure growth continues at a clip for the next few decades. By around mid-century, if the predictions are right, population will for the first time in centuries begin a slow decline.

These are just guesses. Many experts believe the UN's nine billion to be a gross underestimate, and predict 11 billion or 12 billion as more likely.

Previous predictions have been too low: the UN's forecast in the early 1990s was that population would peak in 2050 at 7.8 billion, a level now virtually certain to be exceeded in the next 15 years.

This year, the seven billionth person will not be named; instead, the UN is merely celebrating the arrival on 31 October.

According to the UN, this is because all babies born around the time will be equally marked. But Adnan's family suspect the real reason may be embarrassment. His parents have been bewildered by the way the UN has behaved since singling out their only child for attention. Since that day, they have received almost no communication from the organisation and certainly no support.

"We saw Kofi Annan as almost like a godfather to him," says Adnan's father, Jasminko.

"He held me up when I was two days old, but since then we have heard nothing from them," says Adnan. The disappointment is palpable. Adan's father is unwell, and his pension and a small stipend paid by Sarajevo as long as Adnan remains in education are the family's only income.

For the boy singled out as the five billionth person, the story is remarkably similar. Matej Gaspar is also aggrieved at the way the UN picked him out at birth and then ignored him for the rest of his life. Adnan and Gaspar are friends on Facebook and have discussed what they regard as their unfair treatment.

It would not be surprising if the UN is touchy about its approach to population questions. For two decades, population concerns have been pushed to one side as governments have become increasingly sensitive about the issue.

There are several reasons – fear on the part of rich countries of being seen to attempt to control the fertility of developing nations; an emphasis on other problems, such as diseases, that seemed less intractable; and religion, which took population firmly off the international aid agenda for the whole of George W Bush's US presidency.

Even usually outspoken green groups have censored themselves on the subject, avoiding the question of whether the number of people on the planet has an impact on our ecology in favour of pointing out that the west consumes a far larger share of available resources than the south.

Some of this reticence is well-founded. Previous discussions under the heading of "overpopulation" implied that some of the world's inhabitants were surplus to requirements, an unpleasant suggestion that carried overtones of eugenics. Population experts lament that these fears prevented a frank discussion for years of whether we should be trying to curb the growth of population in our own interests.

Women's rights are central to this framing of the argument. Hundreds of millions of women around the world, but mainly in developing countries, have families bigger than they wish, because they are being denied the ability to control their own reproductive health, according to Population Action International.

Although the planet may be able to support billions more people than are forecast to join us, the question of how all of those new people can live decently, rather than in unnecessary misery, will not be answered by nature or technology but by politics.

Whether our political systems can cope with the strain – of competition for resources, of the distribution of Earth's natural wealth, of the potential for runaway climate change, and of the economic and social crises that will follow – without collapsing into destitution or war is a matter for conjecture.

Asked what he hopes for the seven billionth child, Adnan is unhesitating: "I wish that the birth of the seven billionth child brings peace to the planet."

From someone else, this might sound like a pious cliche. But from Adnan's fourth-floor bedroom window, you can look out to see another block of flats close by. More than 15 years after the war in Bosnia-Herzegovina officially ended, the walls still bear the scars of hundreds of bullets.

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